If one of any of these rivers is contaminated with nuclear material then the whole river is affected and polluted.
1. The fish and marine life in these rivers will be destroyed and they are needed for the ecological preservation of the rivers, irrespective of which way the current flows.
If fish contain nuclear material and these fish or their nuclear infested offspring which swim in or near the Bangladesh-India border (5th longest in the world) and are then consumed by Indian civilians they can die of cancer.
Now this may seem trivial to an RSS-Hindutva fanatic who revels at the thought of killing and slaughtering, and masturbates to the idea of wiping out millions of people with nuclear weapons but in the real world this is something horrific.
If you want, go to Google images and type "Chernoby mutation" and you will see some absolutely appalling images.
However as I said these facts may mean nothing to Hindutva fanatics.
Hindutva fanatics.
2. If these three major rivers and their tributaries are nuked then this will effect the Bay of Bengal, part of which belongs to India itself and where Indian fishermen operate too.
The bay of Bengal contains potentially $5 trillion worth of resources, even if India got 10% of that (assuming it was true) than $500 billion is enough to change the entire economy of west Bengal, Orissa and the north-east, this combats poverty.
Poverty leads to discontent, which can lead to support for the opposition, including armed opposition such as the Naxals.
These Naxals are in 1/3 of all of Indian territory and have been declared by Manmohan Singh, the head of India's government, as the "greatest threat" to India.